Watch for headstock wear and runout. Not the chuck but the threaded or tapered part the chuck fits onto. Can be corrected but bearings are expensive and bushing types are hard to finish correctly. Check for worn or chipped gears. Back gears and engagement parts.

Watch for beat up or worn ways. Slop in cross feed or apron feed screws. Wear in thread making portion of the carriage. Half nut wear at the carriage. Make sure tailstock matches the lathe.

Single or three phase electric. Condition of motor and forward reverse switch.